In an effort to increase spectral efficiency, many state-of-the-art communications systems, including third generation (3G) cellular communications systems such as EDGE (Enhanced Data rates for GSM Evolution) and W-CDMA (Wideband Code Division Multiple Access), employ modulation schemes that produce non-constant-envelope signals. In a traditional quadrature-modulator-based transmitter, the levels of these non-constant-envelope signals are reduced before being introduced to the transmitter's power amplifier (PA), and the PA is configured to operate in its linear region of operation to prevent signal clipping. Unfortunately, this results in an undesirable trade-off between amplifier linearity and power efficiency.
To avoid the amplifier linearity versus power efficiency trade-off, an alternative type of communications transmitter known as a polar modulation transmitter may be used. FIG. 1 is a simplified drawing of a typical polar modulation transmitter 100. The polar modulation transmitter 100 comprises an amplitude modulator 102, a phase modulator 104, and a power amplifier (PA) 106. The amplitude modulator 102 is operable to modulate a direct current power supply signal Vsupply according to envelope information contained in an amplitude modulation (AM) signal received in an AM path of the polar modulation transmitter 100, to generate an amplitude modulated power supply signal VDD(t). Meanwhile, the phase modulator 104 operates to modulate a carrier signal according to angle variations contained in a constant-amplitude phase modulation (PM) signal received in a PM path, to generate a phase modulated carrier signal. The PA 106 is configured to amplify the phase modulated carrier signal while the amplitude modulated power supply signal VDD(t) is applied to a power supply input of the PA 106. Because the phase modulated carrier signal has a constant amplitude, the PA 106 can be implemented as a highly-efficient nonlinear PA 106 without the risk of signal clipping. Typically, the PA 106 is implemented as a switch-mode type of PA (e.g., a Class D, E or F switch-mode PA) configured to operate in compression. Accordingly, the amplitude modulation contained in the amplitude modulated power supply signal VDD(t) is modulated onto the phase modulated carrier signal as the phase modulated carrier signal is amplified by the PA 106.
Another major benefit of the polar modulation transmitter is that its baseband functions can be designed entirely with the use of digital circuits. This allows the design to be fabricated in standard high-yield integrated circuit manufacturing processes, such as the widely used complementary metal-oxide-semiconductor (CMOS) logic process. It also allows digital signal processing techniques to be applied, which are easily adaptable to different modulation standards, thereby providing a multimode capable solution.
FIG. 2 is a drawing of a typical polar modulation transmitter 200 highlighting its digital baseband processing functions. The digital baseband processing functions comprise a baseband processor 202 including a symbol generator 204 and a rectangular-to-polar converter (such as a Coordinate Rotation Digital Computer (CORDIC) converter) 206. The symbol generator 204 functions to generate in-phase (I) and quadrature phase (Q) sequences of symbols from bits in a digital message to be transmitted. The CORDIC converter 206 functions to convert the I and Q sequences of symbols into digital polar-coordinate amplitude and phase modulation signals ρ and θ. After being converted to analog AM and PM signals by AM and PM path digital converters (DACs) 210 and 212, the polar modulation transmitter 200 operates in essentially the same manner as described above in connection with FIG. 1.
Although digitally generating and processing modulation signals in a polar modulation transmitter offers a number of benefits, inaccuracies can occur due to the discrete-time nature of the digital modulation signals. Many existing modulation technologies such as orthogonal frequency division multiplexing (OFDM), and other existing or soon-to-be deployed wireless technologies, such as the Third Generation Partnership Project (3GPP) W-CDMA, Long Term Evolution (LTE) and High-Speed Packet Access (HSPA) technologies that employ wideband signals, exhibit significant signal activity at low magnitudes. When these signals are represented in the form of discrete-time samples, sample-to-sample origin-crossing events occurring in the rectangular-coordinate modulation signal trajectory are not always accurately translated to zero magnitude during the rectangular-to-polar conversion process. This problem is illustrated in FIGS. 3A and 3B, where it is seen that although the rectangular-coordinate modulation signal crosses through the I-Q plane origin in FIG. 3A, after being converted to polar coordinates the magnitude of the amplitude modulation signal ρ never properly reaches zero magnitude, as it should, albeit only for a very brief period of time.
Failing to accurately translate origin-crossing events of a rectangular-coordinate modulation signal to zero magnitude events in the polar domain results in a modulated output signal that incorrectly encircles the I-Q signal plane origin, rather than passing through it, as illustrated in FIG. 4. As shown in FIG. 5, when an origin-encircling event is present, the extra signal energy caused by the signal not crossing through the origin is leaked into adjacent channels 504 (indicated by the dashed lines in the PSD side lobes in the adjacent channels 504). The leaked power can makes it difficult to comply with communications standards specifications such as adjacent channel leakage ratio (ACLR).
It would be desirable, therefore, to have methods and apparatus for addressing inaccuracies produced in polar-coordinate amplitude modulation signals caused from representing the amplitude modulation in the form of discrete-time samples.